Combine 3 tbsp honey and 3 tbsp water in a small saucepan. Add the sliced fresh ginger. Warm over low heat, stirring until honey dissolves and mixture is just simmering (do not boil) for 3–4 minutes to infuse ginger. Remove from heat and let steep for 10–15 minutes for stronger flavor. Strain out ginger and transfer syrup to a jar. Cool to room temperature before using. Refrigerate leftover syrup up to 2 weeks.

Prep Glass

Place 1 tsp superfine sugar on a small plate. Run a lemon wedge around the outer rim of a chilled coupe or martini glass to moisten. Dip the rim lightly into the sugar to create a delicate sugared edge. Set glass aside.

Cocktail Assembly

Fill a cocktail shaker with ice (about 1 cup).

Add 2 oz Hendrick's Gin, 0.5 oz Grand Marnier, 0.75 oz fresh lemon juice, and 0.5 oz honey-ginger syrup to the shaker.

Shake vigorously for 12–15 seconds until the shaker is very cold and well-chilled, producing a slight froth from the honey.

Double-strain the cocktail into the prepared chilled coupe or martini glass to remove ice chips and any remaining ginger bits.

Garnish with a thin lemon wheel or a long twist of lemon peel floated on top or perched on the rim. Serve immediately.